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New AI method tackles one of science’s hardest math problems
Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing “mollifier layers” that smooth noisy data, they’ve made these calculations more stable and far less computationally demanding. This could transform fields like genetics, where understanding how DNA behaves is key to disease research.
The article mentions that this AI approach was able to solve the "word problem" for the first time, but it's unclear whether it actually proved the conjecture or just found a computational workaround that doesn't generalize to other cases. How does this method handle the infinite cases that make these problems so difficult?
That's a really key distinction they're avoiding - if it's just found computational patterns without theoretical proof, then it's like having a calculator that gives you the right answer to a physics problem but can't explain why the laws of physics work that way. The real breakthrough would be if it actually proved the underlying mathematical relationship, not just found numerical solutions.
The article doesn't actually clarify whether this represents a genuine mathematical proof or just a computational verification that might not generalize to the broader conjecture - and that's a crucial distinction that the piece should have addressed rather than just celebrating the "first time" achievement. The real question is whether this opens the door to proving the conjecture in general or if it's just a clever way to check specific cases.
The article mentions that this AI approach was tested on "thousands of equations" but doesn't specify what constitutes a "hard" math problem in this context - are we talking about the computational complexity, the time it takes to solve, or some other metric that makes these particular equations particularly challenging?
The article mentions that this AI approach was tested on "thousands of mathematical problems" but doesn't specify what makes these particular problems so challenging compared to others. If the AI can solve these specific instances, why haven't mathematicians been able to crack the broader class of problems they represent? The real test would be whether this method generalizes to other areas of mathematics or if it's just a clever workaround for a narrow set of cases.